Question

xialoli was estimating the difference between two positive numbers x and y (where x>y). First she rounded x up by a small amount. Then she rounded y down by the same amount. Finally, she subtracted the rounded values. Which of the following statments is correct? a) her estimate is larger than x-y. b) her estimate is smaller than x-y. c) her estimate equals x-y. d) her estimate equals y-x e). her estimate is 0. f) this is not enough information to compare x-y with her estimate. (show work please )

Answer 1

Remark

This is an excellent question. Estimation is a powerful skill to have. People should always shop using estimates. Try it to see what happens.

x = 11.7 which rounds up to which we will call x1 and that is 12

y = 6.03 which round down to 6 which we will call y1 and that is 6

Now x - y = 5.67

If you do the rounded subtraction x1 - y1 = 12 - 6 = 6

The estimate is not zero. D is not correct.

There is enough information E is not the answer.

B is wrong, her estimate is larger than x - y

C is wrong the two subtractions are not equal.

A is correct and always will be no matter what numbers are chosen

A <<<< Answer